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Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
- V. Batyrev
- Mathematics
- 1 October 1993
We consider families ${\cal F}(\Delta)$ consisting of complex $(n-1)$-dimensional projective algebraic compactifications of $\Delta$-regular affine hypersurfaces $Z_f$ defined by Laurent polynomials…
Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties
- V. Batyrev, D. Straten
- Mathematics
- 30 July 1993
We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV1,...,Vr in a toric…
On the Hodge structure of projective hypersurfaces in toric varieties
- V. Batyrev, David A. Cox
- Mathematics
- 25 June 1993
This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces. Given a $d$-dimensional projective simplicial toric…
New Trends in Algebraic Geometry: Birational Calabi–Yau n -folds have equal Betti numbers
- V. Batyrev
- Mathematics
- 16 October 1997
Let X and Y be two smooth projective n-dimensional algebraic varieties X and Y over C with trivial canonical line bundles. We use methods of p-adic analysis on algebraic varieties over local number…
Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs
- V. Batyrev
- Mathematics
- 16 March 1998
Using non-Archimedian integration over spaces of arcs of algebraic varieties, we define stringy Euler numbers associated with arbitrary Kawamata log-terminal pairs. There is a natural Kawamata…
Manin's conjecture for toric varieties
- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 October 1995
We prove an asymptotic formula conjectured by Manin for the number of $K$-rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth projective toric…
ON THE CLASSIFICATION OF SMOOTH PROJECTIVE TORIC VARIETIES
- V. Batyrev
- Mathematics
- 1 December 1991
Strong McKay correspondence, string-theoretic Hodge numbers and mirror symmetry
- V. Batyrev, D. Dais
- Mathematics
- 4 October 1994
Tamagawa numbers of polarized algebraic varieties
- V. Batyrev, Y. Tschinkel
- Mathematics
- 1 December 1997
Let ${\cal L} = (L, \| \cdot \|_v)$ be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety $V$ defined over a number field. Denote by $N(V,{\cal L},B)$ the number of…
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